The question of whether or not a large-scale quantum computer will be built is a concern to the security world. This is due to the fact that large-scale quantum computers, if built, will be able to break the standard asymmetric cryptographic schemes in wide use today—namely, RSA and discrete log (over finite fields and Elliptic curves). As such, the cryptography world is preparing for this possible eventuality (e.g., NIST is now running a process to standardize post-quantum secure algorithms).
One of the leading techniques for achieving post-quantum secure asymmetric encryption is lattice-based cryptography. A lattice is a type of group (loosely speaking, a group is a mathematical object that supports an operation between objects and closure). A lattice is defined by a series of base vectors B={b1, . . . , bn}, and the lattice itself is all of the integer linear combinations of these vectors. Lattices come with some problems that are thought to be very hard (i.e., cannot be solved efficiently), for example given a basis B find the shortest (or close to shortest) vector in the lattice, or given a basis B and a vector v find a vector that is close to v. Lattice-based cryptography has the property that if the underlying problem is indeed hard, the cryptographic scheme is provably secure. Importantly, these problems are thought to be hard even for quantum computers. Thus, lattice-based cryptography is a good candidate for post-quantum asymmetric cryptography. There are a number of encryption algorithms that are based on lattices, and are assumed to be post-quantum secure. Some examples are the GGH encryption scheme, NTRUencrypt, and LIMA.